iii. ii. iv. i. a) Using Routh Hurwitz criterion, based on the transfer function of 1 5+65 +115 + 6s+k i. ii. i. b) Consider a characteristic polynomial, ii. T(s) = Determine the value of k to ensure the stability of the system. Determine the value of that causes the system to be marginally stable. QUESTION 3 (25 marks) a) Sketch the root locus of a feedback system with a characteristic equation of K(+1) S+25-3 R(s). q(s) = 8 + s + 45 +24s + 3s +63 Using Routh Hurwitz table, determine how many poles are there in the right half plane, in the left half plane and on the jo-axis. Is the system stable? Explain. 1+ b) A feedback control system is shown in Fig. 3. K =0 Fig. 3 $+1 s(s+2)(s+3) Y(s) Plot the pole(s) and zero(s) of the system on the s-plane. Calculate and sketch the centroid and the asymptotic line(s). Determine the breakaway/in point (s). Find the imaginary axis crossing point(s). Justify your answer. Sketch and refine the root locus of the system. (3) (11) (2) (25 (